The GIANTS shocked the AFL world with their 32-point victory at Spotless Stadium on Saturday and are sure to face a fired-up Swans outfit when they next meet, in round 15 at the SCG.
According to Shaw, GWS intends in that game to "keep the foot on the throat" of their far more heralded rival.
"The rivalry is definitely there and it's building even more so," Shaw said during a visit to Campbelltown Hospital as part of the Slater & Gordon Gentle GIANTS program on Tuesday.
"For us to get a win first-up in the season, it's pretty exciting stuff, and I think later in the year when we play them again it's going to be on.
"They're going to want redemption and we're going to want to keep the foot on the throat like we did on the weekend.
"That's exciting times and it's exciting for Sydney to build up the code as much as we can and build that rivalry."
Recruit Lance Franklin has drawn some stinging criticism after his one-goal Swans debut in the wet at Sydney Olympic Park, with some already suggesting the two-time Coleman medallist is past his best.
Instead, it was GWS' young key forwards Jeremy Cameron (four goals) and Jonathon Patton (three) stealing the show.
Franklin was linked with GWS throughout 2013 before joining the Swans and while Patton said on Tuesday it "would've been nice" to sign him, he also stated "I don't think we really need him at all".
That is due to the bountiful stocks of young talent GWS already possesses, with last year's No.1 pick Tom Boyd and athletic forward Adam Tomlinson among those still waiting in the wings.
But Shaw, the former Collingwood defender who enjoyed some epic battles with Franklin's Hawthorn side over the years, is still backing the superstar to have a huge year with his new club.
"We put a lot of time and effort into nullifying (Franklin) because we know how good a player he is," Shaw said.
"It wouldn't surprise me if at the end of the year you look back and Buddy's kicked 80 goals.
"It's something that he's obviously working on and the Swannies are working on, but it's one game into it.
"I wouldn't write him off just yet."
Shaw enjoyed the victory and getting a win over his brother, Swans defender Rhyce Shaw, but he knows the work has only just begun.
GWS might have to deal with the unfamiliar position of being the favourite when it travels to Etihad Stadium to take on St Kilda in round two.
"I won't say it's the best win I've ever had because I've had a couple of good ones, but it was right up there," the premiership-winning defender said.
"We went in knowing we probably have to play our best footy to beat the Swannies because they are a good team.
"To do it the way we did was great for everyone and a reward for all the work these boys have put in.
"It's one game done, you tick that off and move on, and we've got a big game coming up in two weeks' time and we've got to back it up.
"The pressure is going to be on us to perform again and that's what we're looking forward to."
